Synergistic-potential engineering enables high-efficiency graphene photodetectors for near- to mid-infrared light

High quantum efficiency and wide-band detection capability are the major thrusts of infrared sensing technology. However, bulk materials with high efficiency have consistently encountered challenges in integration and operational complexity. Meanwhile, two-dimensional (2D) semimetal materials with unique zero-bandgap structures are constrained by the bottleneck of intrinsic quantum efficiency. Here, we report a near-mid infrared ultra-miniaturized graphene photodetector with configurable 2D potential well. The 2D potential well constructed by dielectric structures can spatially (laterally and vertically) produce a strong trapping force on the photogenerated carriers in graphene and inhibit their recombination, thereby improving the external quantum efficiency (EQE) and photogain of the device with wavelength-immunity, which enable a high responsivity of 0.2 A/W–38 A/W across a broad infrared detection band from 1.55 to 11 µm. Thereafter, a room-temperature detectivity approaching 1 × 109 cm Hz1/2 W−1 is obtained under blackbody radiation. Furthermore, a synergistic effect of electric and light field in the 2D potential well enables high-efficiency polarization-sensitive detection at tunable wavelengths. Our strategy opens up alternative possibilities for easy fabrication, high-performance and multifunctional infrared photodetectors.


REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): In this manuscript, Qiu et al. show a very interesfing example of near-to mid-infrared photodetector based on graphene.I appreciated very much reading their manuscript and I recommend its publicafion in Nature Communicafions.I would only ask the authors to address the following points: -I understand that all the fabricafion steps have been moved to the methods secfion, however, while reading the text, it is difficult to understand how the heterostructure of their detector is formed.I suggest summarizing in a brief sentence what device they propose (e.g.graphene wet-transferred on dry-pafterned silicon-on-insulator [...]) before diving into the device characterizafion.
-I suspect that graphene is suspended when transferred on such a narrow slit.Have the authors taken this into account in their device analysis?-Please double-check acronyms: R is never introduced as responsivity (see line 202) and HWP is never defined.
-The authors use a device which is in a photoconducfive configurafion.This means a higher dark current compared to photodiodes, photo-thermoelectric devices, etc.It would be nice if the authors could briefly comment on this.
-I find the valley and peak nomenclature a bit counterintuifive as, the most important parameter, i.e., the photocurrent/responsivity/detecfivity, is, in fact, higher in the valleys and smaller in the peaks.

Reviewer #2 (Remarks to the Author):
The manuscript presents an interesfing implementafion of a layered material-based device where the electrical gain and light field tuning effects are combined in order to increase the responsivity and to extend the working range toward the long(er) wavelength.
There are significant noteworthy results, especially looking at the high responsivity reported for the longer wavelengths (measured with a blackbody radiafion source).
The work is sufficiently novel, however, there are reported devices which recall the structure demonstrated here.
There is a substanfial lack of informafion in the main arficle but especially in the supporfing material(see below for details).
The soundness of the methodology is difficult to assess because of the lack of informafion menfioned before.
Because of the previous points, the fabricafion of the device can be replicated, while replicafing the actual results and relafive tests will be not straighfforward.
Here is a list of specific comments which I believe have to be addressed.1)There are too many qualitafive adjecfives that, in this scienfific context, don't carry valuable informafion, prevent clear understanding and repeatability and benchmarking.
2)Most of the fundamental physics behind the device's working principle is only described qualitafively without sufficient modelling/simulafion/references.3)Figure 1d the simulafion seems to show an asymmetric behaviour in an otherwise (apparently)symmetric structure 5)Most of the figures and plots are not fully readable and in low-quality 6)The responsivity menfioned is expressed without any further informafion on the characterizafion condifions: applied source-drain voltage, condifion of the illuminafion, spot shape and size, etc.This info are also missing in the supplementary material 7)The capfion of figure2 starts by saying "simulafion…."But the overall picture does not include mainly simulafion.8)Blackbody radiafion measurements have several conceptual gaps.To menfion a few: how are the other effects that can induce a variafion in the graphene resistance taken into account (thermal, strain, etc )? 9)Supplementary material: the "Surface Electric Field Engineering and Gain model" is mainly a standard model for pn juncfion in and out of equilibrium.The authors should explicitly adapt the model to the actual device under test.10)No measurements of the graphene have been carried out.Raman, doping, strain and resisfivity should be carried out.If some of them are not possible, at least proper characterizafion of the resisfivity should be done.11) Supplementary informafion: secfion" Transient photoresponses of graphene/2D slit structure photodetector upon different wavelength".The chopper speed is properly set to show the transient.Hence this can't be properly observed/quanfified. 12)Supplementary material: in Table S2, several working principles are compared together: this comparison requires supporfing evidence and explanafions in order to give the tools to the reader to understand the quanfifies.
I believe that in its current status, the paper should not be accepted.

Reviewer #3 (Remarks to the Author):
This manuscript fitled "Synergisfic-Potenfial Engineering Enables High-Efficiency Graphene Photodetector for Near to Mid-infrared light" by Jiang et al reported the design and fabricafion of graphene infrared photodetector based on 2D silicon-on-insulator substrate.The 2D potenfial well created by the pafterned silicon block matrix can effecfively trap photoexcited carriers and enable high photoconducfive gain.In addifion, by designing the silicon matrix for polarized detecfion, the detector showed highly polarized photo response for 1.55 um incident light.Finally, the detector was tested for detecfing blackbody radiafion from 500 K to 1000 K with high responsivity and detecfivity.This manuscript provided a new design for enhanced infrared photodetecfion of graphene photodetector.The pafterned silicon substrate is compafible with semiconductor processing technology, and the design can be tailored for various bands.Therefore, this manuscript is of great important for graphene infrared photodetectors.I would recommend its publicafion after the following comments are properly addressed in the revised manuscript.1.The trapping of carriers by the potenfial well is crucial for the high responsivity, and the recombinafion lifefime is an important parameter.Can the authors measure or esfimate the prolonged the carrier lifefime compared with convenfional graphene/Si juncfion?2. The detector showed responsivity up to 38 A/W.Is this high responsivity mainly from the long carrier lifefime or enhanced absorpfion?Did the authors measure the absorpfion of the device?3. To achieve polarized detecfion, the silicon needs to be pafterned for polarizafion sensifive response, however, the responsivity is much lower than that shown in Figure 2. It seems the 2D potenfial well and the polarized detecfion can not be aftained simultaneously.Please comment on this. 4. For blackbody detecfion, the responsivity increases with temperature.Since the radiafion power also increases with temperature, this trend is opposite to the normally observed decreasing responsivity with incident power.Did the author measured power dependent responsivity for 1.55 um or other wavelength? 5. Table S2 is not complete.6.What was the source-drain voltage and the corresponding electric field?
Reply to the reviewers: Reviewer 1

Comments:
In this manuscript, Qiu et al. show a very interesting example of near-to mid-infrared photodetector based on graphene.I appreciated very much reading their manuscript and I recommend its publication in Nature Communications.
Author Reply: We appreciate the reviewer's positive feedback on this work and the valuable suggestions provided.We have made revisions and additions as per each point, including the inclusion of necessary figures and tables, as detailed below.
1.I understand that all the fabrication steps have been moved to the methods section, however, while reading the text, it is difficult to understand how the heterostructure of their detector is Author Reply: We appreciate the suggestions made by the reviewer.In the main text, there was indeed a lack of extensive elaboration on the device fabrication process, which left readers with a sense of information deficit.Consequently, we have supplemented this deficiency with detailed process flowcharts for device fabrication as shown in Figure R1.1.To summarize in short sentences: Graphene is wettransferred onto dry-patterned silicon-on-insulator and connected to the source and drain electrodes to serve as the channel.
Author action: We have added an explanation "Regarding the device structure, graphene is wet-transferred onto dry-patterned silicon-on-insulator and connected to and drain electrodes to serve as the channel (Fig 1b)." about the device structure on page 3 of our manuscript.Additionally, we have included Figure R1.1 in the supplementary information as Figure S3, along with an accompanying image description.The detailed description of the fabrication process can be found in Method.

I suspect that graphene is suspended when transferred on such a narrow slit. Have the authors taken this into account in their device analysis?
Author Reply: In the experimental process, we also utilized AFM characterization to compare and determine the state of graphene on the structural surface.In this context, in the grating structure with the maximum duty cycle, when the grating height is 160 nm with a 200 nm spacing, graphene is less likely to be suspended.Furthermore, after wet transferring graphene onto the substrate structure, two annealing steps were performed, with the second annealing being particularly crucial.The 12-hour annealing process at 300°C had been conducted to ensure that graphene makes full contact with the substrate structure.AFM characterization was conducted to confirm the conformation of graphene with the substrate, as shown in the Figure R1.2, it can be observed that graphene approached a nearly conformal relationship with the grating structure.responsivity as disadvantages.Photoconductive devices based on the photogating effect primarily rely on the separation and recombination of charge carriers in vertical heterojunctions or traps to generate a gain, necessitating operation under bias voltage, hence achieving high responsivity.This, however, leads to the challenge of elevated dark current, which requires addressing in future work.In this paper, the non-uniform distribution of heterojunctions to some extent helps suppress the dark current in the graphene channel.These discussions indeed need to be summarized at the end of the paper.
As the reviewer has pointed out, different types of devices need to be discussed and compared separately, as shown in the table below.All these devices depend on graphene for light absorption, making photoconductive devices with gain advantageous for broad-spectrum detection.Our research harnesses the synergistic interaction between optical and electrical fields, enabling us to surpass the performance advantages documented in existing literature.Author action: We have updated Table S4 in the supplementary information and added relevant explanations.
5. I find the valley and peak nomenclature a bit counterintuitive as, the most important parameter, i.e., the photocurrent/responsivity/detectivity, is, in fact, higher in the valleys and smaller in the peaks.
Author Reply: Sorry for the confusion caused by the previous definitions.As pointed out by the reviewer, the names of peak and valley are not appropriate.After careful consideration, we can refer to the points with the strongest and weakest reflections as R point and A point., as shown in Figure R1.4.

Author action:
We have redrawn Figure 3 in the manuscript and revised the relevant instructions.Reviewer 2 Comments: The manuscript presents an interesting implementation of a layered material-based device where the electrical gain and light field tuning effects are combined in order to increase the responsivity and to extend the working range toward the long(er) wavelength.
There are significant noteworthy results, especially looking at the high responsivity reported for the longer wavelengths (measured with a blackbody radiation source).
The work is sufficiently novel, however, there are reported devices which recall the structure demonstrated here.
There is a substantial lack of information in the main article but especially in the supporting material (see below for details).
The soundness of the methodology is difficult to assess because of the lack of information mentioned before.
Reply: We greatly appreciate the reviewer's valuable questions, which highlight certain shortcomings in the depth of analysis and completeness of information in the paper.This has inspired us to make comprehensive revisions to the figures, tables, expressions, theoretical models, and missing information in the manuscript.In response to the reviewer's queries, in the revised manuscript, we have systematically reorganized the physical processes underlying the device operation.Additionally, we have provided comprehensive details on device simulation, fabrication, and testing, while also enhancing the clarity and refinement of the figures and corresponding descriptions throughout the entire document.We believe that these improvements, compared to the previous version, have significantly enhanced the paper, and we are thankful for the reviewer's insightful comments.Below are the itemized modifications addressing the reviewer's questions.
Comments 1: There are too many qualitative adjectives that, in this scientific context, don't carry valuable information, prevent clear understanding and repeatability and benchmarking.
Reply 1: We highly appreciate the invaluable questions raised by the reviewer.We have undertaken a thorough reevaluation and understanding of the phenomena and underlying mechanisms in our work, and have made revisions in the following areas to enhance the quality of the manuscript for clear understanding and repeatability and benchmarking: 1. We have undertaken a rephrasing of some of the qualitative descriptions in the mechanism explanation of Figure 1, and have categorized the associated physical processes into three distinct stages, as elaborated in detail in in Supplementary Note 2.
2. For the repeatability and rationality of the work, we have added a detailed device preparation method flowchart and detailed testing conditions in Supplementary Note 1 and Supplementary Note 6 3. Added detailed performance characterization of the device, such as absorption spectra and carrier lifetime.

Author action:
We have rewritten the various parts of the manuscript and highlighted them in red.
Comment 2: Most of the fundamental physics behind the device's working principle is only described qualitatively without sufficient modelling/simulation/references.

Reply 2:
We appreciate the questions raised by the reviewer.We have systematically reviewed and sequentially described the physical processes governing the operation of the device.In this paper, the primary physical principles underlying this work can be mainly categorized into the electrical gain induced by fluctuating potential and the artificial anisotropic absorption resulting from specific optical grating structures.We applied Silvaco TCAD for electrical simulations and employed COMSOL for wave optics simulations to elucidate the device's operational mechanisms.In response to the questions, we have undertaken a detailed modeling and exploration of the device's operational mechanisms, and have made the following modifications:

Electrical gain analysis
The generation of electrical gain involves three main physical processes: the first is the generation of potential wells, the second is the separation of photocarriers, and the third is the process of photoconductive gain.

Generation of potential wells
It has been discovered that a strong electric field is located at the edge of silicon and silicon oxide, which would be stronger than the built-in electric field formed by graphene and silicon, which can be modeled and simulated in Figure R2.1 by Silvaco TCAD.For the slit structure, due to the electric field coupling between adjacent grating boundaries, the surface potential distribution will resemble a valley with a higher potential difference, as shown in the corresponding schematic diagram of Figure S5c.This potential distribution caused by the slit structure can be called the slit effect.Furthermore, when a slit structure is constructed in two mutually perpendicular directions in a two-dimensional plane, the valley potential distribution will evolve into a 2D potential well.  ) where z=0 is the interface between silicon and graphene,  is the width of depletion zone at the interface,  =   −   is the net carrier concentration of silicon, where   is the donor impurity concentration,   is the acceptor impurity concentration, and   is the dielectric constant of silicon.
The corresponding expression of the contact potential can be obtained by: Since graphene will not have large Fermi level shift when contacting with silicon oxide, the electric field of homojunction ψ s − is equal to the edge strong electric field.
Next, under the action of electric potential ψ s − and ψ s − , the photocarriers in graphene are separated and form photocurrent.For convenience, we will refer to the two sides with potential differences as the P-type region and N-type region, respectively.For the carrier distribution in the heterojunction region, the relationship between carrier concentration of P-region and quasi Fermi level is thus At the boundary of P region, we define  = −  ,  −   = , so Because   (−  ) is the majority carrier in the P-type region, so   (−  ) =  0 ，  0  0 =   2 , Thus, at the boundary of P-type region  = −  , minority carrier concentration at P region is Thus, the photo-generated minority carrier concentration injected into the P-type region is obtained Similarly, the photo-generated minority carrier concentration injected into Ntype region at the boundary  = −  is It can be seen that the photo-generated minority carrier at the boundary of the injection barrier region is a function of the applied voltage and also a boundary condition for solving the continuity equation.
In the steady state, the continuity equation of photo-generated minority carriers in the hole diffusion region is In the case of small injection   = 0 The variation of carrier concentration in P and N regions can be solved: where  = (  −   ) =  i .  =   −   ，   is contact potential difference or built-in potential difference due to the difference of Fermi energy levels of junctions in the dark state, where   comes from the photogenerated voltage where  () is the injection concentration of electrons (holes),  0 is the intrinsic carrier concentration,   (  ) is the mobility of electrons (holes), E is the applied electric field.g is the generation rate of excess carriers.L is the length of graphene channel.  is the barrier height due to the difference of Fermi energy levels of junctions in the dark state   (  ) is the diffusion length of carrier.
It is also assumed that the holes in the diffusion length   and the electrons in   can diffuse to the other side of the pn junction.Then the photogenerated current is Where  ̅ is represented as the average generation rate of photo-generated carriers within the diffusion length (   +   ) of the junction.The interface voltage of heterojunction can be derived where   is the reverse saturation current, and   ∝ ψ s − + ψ s − .

Photoconductive gain
Under the influence of the interface electric field, one type of photocarriers is separated to the potential well region, while the other type of photocarriers, under the bias effect, undergo photoconduction within the graphene channel, resulting in photocurrent generation.The potential well traps photogenerated electrons/holes, thereby extending their recombination time.As a result, multiple conduction cycles occur within the channel before the recombination of photocarriers, leading to gain.
We refer to this process as the photogating effect.
According to the Gain expression based on photogating effect (Fang, H. & Hu, W. Advanced science 4, 1700323 (2017).) The formed built-in electric field not only promotes the separation of photogenerated carriers in graphene, but also inhibits the recombination of photogenerated carriers, which can induce cyclic gain.After derivation with R16, the gain can be expressed as: When there is no applied voltage on the junction, ∝  .Thus, the enhancement of the built-in potential can lead to the increase of the gain.Here, the separation driving force of photo-generated carriers is provided by the surface lateral electric field and the vertical heterojunction built-in electric field.Therefore,   ∝ ψ s − + ψ s − .

Optical analysis
Throughout the entire process of photodetection, the first step involves the incidence and absorption of light, while the second step involves the conversion of light into an electrical signal (mentioned above).Therefore, for polarization-sensitive detection, this is achieved through the polarization ratio of incident and absorbed light.As the reviewer has pointed out, different types of devices need to be discussed and compared separately, as shown in the table below.All of these devices rely on graphene for light absorption, and, therefore, for broad-spectrum detection, photoconductive devices with gain prove to be advantageous.Our work leverages the synergistic interaction of the optical and electrical fields to break through the performance advantages reported in existing literature.  5. Table S2 is not complete.
Author Reply: We appreciate the reviewer's reminder, and we have improved and categorized the Table S2 while adding a systematic discussion of devices with different working mechanisms as Table R3.1.
formed.I suggest summarizing in a brief sentence what device they propose (e.g.graphene wettransferred on dry-patterned silicon-on-insulator [...]) before diving into the device characterization.

Figure R2. 1
Figure R2.1 Surface potential simulation.(a) 3D structural modeling.(b) Surface electric field distribution map.(c) The relationship between surface electric field and position.

Figure R2. 4
Figure R2.4 (a)-(c) The polarization sensitive reflection spectra of structures with DC of 0.3, 0.35, and 0.4 measured by FTIR.The illustration shows the corresponding far-field simulation results.The grating height is 160 nm, the unit length is 1 µm

Figure R2. 7 .
Figure R2.7.Studies on the electric field distribution induced by slit structure.

Figure R3. 4
Figure R3.4The relationship between device responsivity and 1.55 μm laser power density Additionally, we have added the relationship between device responsivity and 1.55 μm laser power as Figure R3.4,as mentioned by the reviewer, which exhibits a linear decay relationship on a logarithmic scale.Author action: We have added the Figure R3.4 as Figure S10 in Support Information.

Table R1
Summary of device parameters of several typical graphene/semiconductor photodetectors previously reported, and our own device.
We appreciate the questions raised by the reviewer.The device type in this paper is a photoconductive device based on the photogating effect, distinct from photodiodes and photo-thermoelectric devices, each of these three device types has its Comment 11.Supplementary material: in TableS2, several working principles are compared together: this comparison requires supporting evidence and explanations in order to give the tools to the reader to understand the quantities.Reply 11:

Table R2 . 3
Summary of device parameters of several typical graphene/semiconductor photodetectors previously reported, and our own device.

Table R3 . 1
Summary of device parameters of several typical graphene/semiconductor photodetectors previously reported, and our own device.